Pit your wits against young minds!

This column is a place for those bits of contagious mathematics that travel from person to person in the community, because they are so elegant, suprising, or appealing that one has an urge to pass them on. Contributions are most welcome.     

An experiment with arithmetic precision in linear algebra computations

Several techniques for experimental determination of floating point precision in practical computations are examined, and applied to linear algebra algorithms. These techniques are simple enough to be directly applicable to existing production codes, requiring a very limited amount of software on many machines, and yet they yield interesting information on the numerical precision of a computation. Our choice of linear algebra algorithms includes a direct solver (namely the MA32 program from the Harwell Library) and several variants of preconditioned conjugate gradients (the methods DIAG, INV, MINV and POL of Reference 1). The results may be of interest as method selection criteria, and thus complement Mflop performance data available from several sources.     

Investigation of MFTIR infrared spectra of peat waxes with sorbed cationic surfactants

Journal of Applied Spectroscopy -     

Clathrate formation in the tetraisoamylammonium propionate-water system

In this paper we examine clathrate formation in the tetraisoamylammonium propionate-water binary system. We have found formation of four polyhydrates, two of which are metastable over the whole temperature range studied. All polyhydrate crystals were isolated and their compositions and densities determined; for (i-C₅H₁₁)₄NC₂H₅COO·36.5H₂O, unit cell parameters were additionally found. The results are compared with data for tetra-n-butylammonium carboxylate polyhydrates, and the structure of the title compounds is suggested. It is confirmed that the isoamyl radical stabilizes the tetradecahedral void of the clathrate hydrate framework better than the n-butyl radical. Institute of Inorganic Chemistry, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 35, No. 3, pp. 67–71, May–June, 1994. Translated by L. Smolina     

Particularities of the dose distribution in irradiated plastic tubing

This paper presents the results of an experimental study undertaken on the irradiation process of polyethylene tubing in an electron beam. Isodoses of distribution through material thickness in case of irradiation in one or two irradiation directions have been analyzed.     

Structural changes in discotic samples during transition from crystal to discotic mesophase as revealed by electron microscopy and diffraction

Classical methods of structural analysis cannot be applied to liquid crystals because higher order reflections disappear during the transition from crystal to liquid crystal due to the reduction in long range orientational and translational correlations. However, in order to relate physical properties to the molecular architecture, it is essential to have information about molecular positions and orientations in the crystalline state as well as in the liquid crystalline state. In this work, the transition from crystalline to liquid crystalline phase is carefully monitored and the relationship between the original lattice and the new molecular positions found using electron diffraction. In addition to this, a new high resolution electron-microscopic technique is described in which the positions of molecules in the crystalline and the quenched discotic phase are directly imaged and the defects observed in the crystalline and LC phase compared and quantitatively analysed.     

Di[2-(4-substituted-phenyl)-3-mercapto-propenato]-nickel(II) complexes. Metallo-mesogens exhibiting broad nematic ranges

Di[2-(4-substituted-phenyl)-3-mercapto-propenato]-nickel(II) complexes have been synthesized and investigated. All of them are mesomorphic; they have nematic phases with wide ranges and typical Schlieren textures.     

The nitrogen pentoxide dissociation equilibrium

The third-law method is used to assess the authenticity of available equilibrium constants for the thermal dissociation of N₂O₅ ? NO₂ + NO₃. © 1994 John Wiley & Sons, Inc.